Question

What is the equation in slope-intercept form for a line that passes through the points (-3, 6) and (9, 10)?
Responses
A
y = 1 x + 5
3
y = 1 x + 5 3
B
y = 1 x + 7
3
y = 1 x + 7 3
C y = 3x + 15y = 3 x + 15
D y = 3x – 3

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b) that passes through the points (-3, 6) and (9, 10), we first need to calculate the slope (m) using the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (-3, 6) and (9, 10):
- \(x_1 = -3\), \(y_1 = 6\)
- \(x_2 = 9\), \(y_2 = 10\)

Substituting these values into the slope formula:

\[
m = \frac{10 - 6}{9 - (-3)} = \frac{4}{9 + 3} = \frac{4}{12} = \frac{1}{3}
\]

Now, we have the slope \(m = \frac{1}{3}\).

Next, we use one of the points to solve for the y-intercept (b) using the slope-intercept form equation \(y = mx + b\). We can use the point (-3, 6):

\[
6 = \frac{1}{3}(-3) + b
\]

Calculating this gives:

\[
6 = -1 + b
\]
\[
b = 6 + 1 = 7
\]

Now we have both the slope and y-intercept. The equation of the line is:

\[
y = \frac{1}{3}x + 7
\]

Thus, the answer is:

**B: \(y = \frac{1}{3}x + 7\)**